Questions tagged [kerr-metric]

The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole.

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How to determine the Delta-v for orbital changes around a Kerr black hole?

What's the Delta-v required to change between the Marginally bound orbit and the innermost stable circular orbit around a Kerr black hole.
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How do we determine whether a surface is an event horizon? Exactly what to calculate to do this?

Event horizons play an important role in relativistic astrophysics, especially for black holes, but also for other spacetimes. It is fundamental to be able to determine whether a given surface is an ...
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Are metrics of general relativity tested?

We tested general relativity with effects as gravitational lensing and existence of black holes (Schwarzschild metric). But there are other metrics, e.g. Kerr-Newman metric for a point mass with ...
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Reference for list of the non-zero, unique components of the Riemann tensor for the Kerr metric

Does there exist textbook or webpage which has a list of the unique components of $R^{\mu}_{\nu \alpha \beta}$ for the Kerr metric? Such a reference is easy enough to find for Schwarzchild (including ...
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How can the ratio of a black hole's (or any object's) angular momentum to its mass be less than one?

In the latest Quanta Magazine article, about Kerr black holes, the researchers say their new solution for these objects only works, so far, for Kerr black holes with a ratio of angular-momentum-to-...
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How to plot off-equatorial orbits in Kerr metric?

I am trying to plot the time-like trajectories in Kerr metric. I have taken the equations from here. I am trying to reproduce the off-equatorial trajectories from Chandrasekhar's textbook, e.g., the ...
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What unit of measurement are used for 𝑀 and 𝑟 in the Schwarzschild metric?

So I understand that 𝑀 in any metric solution stands for mass. But what unit of measurement do you use to define 𝑀?
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Are rotating black holes producing a frame dragging effect inside the event horizon?

Are rotating black holes producing a frame dragging effect inside the event horizon? Is that effect moving space inside the event horizon at speeds far greater than the speed of light?
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What is the physical interpretation and differences between static and stationary observers in Kerr geometry?

The geometry around a rotating uncharged axially-symmetric black hole is described by the Kerr metric. Being stationary and axisymmetric, the Kerr metric admits two Killing vector fields: $$\partial_t=...
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Doubt regarding 4-velocity of a particle in Kerr space-time

The Kerr metric written in Boyer-Lindquist coordinates is: $$ds^2=-\frac{\Sigma\Delta}{A}dt^2+\frac{A\sin^2\theta}{\Sigma}(d\phi-\omega dt)^2+\frac{\Sigma}{\Delta}dr^2+\Sigma d\theta^2$$ where $\Sigma=...
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Why is polar ($z$-axis) symmetry assumed in Kerr Black Holes?

In O'Neill's "The Geometry of Kerr Black Holes" he explicitly states that the $z$-axis has a ± isometry; a.k.a. Z2 symmetry of reflection in z=0 plane that exchanges south and north ...
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Is the curvature of spacetime zero, in the center of a Kerr black hole?

In a Kerr black hole the singularity in the center has become a ringularity. Roughly said a singularity that is not point-like but circle-like. The curvature blows up not at the exact center of the ...
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What does the Penrose diagram of a super extremal black hole (naked singularity) looks like?

What does the Penrose diagram of a super extremal black hole (naked singularity) looks like? I have seen the ones for regular charged/rotating black holes, but I can't find a good clear one for super ...
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How to plot Kerr geodesics?

In $ x^{\mu}= \{t,\rho,\theta,\phi\}$Boyer-Lindquist coordinates the Kerr solution takes a manageable form. Given some initial conditions $x^{\mu}(\lambda=0)$ and $\dfrac{dx^{\mu}}{d\lambda}(\lambda=0)...
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Does an observer falling into a kerr black hole see the universe rotate an infinite number of times? [duplicate]

Does an observer falling into a Kerr black hole see the universe rotate an infinite number of times? Since to an outside observer it takes infinite time to fall into a blackhole, if the hole is a Kerr ...
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Wouldn't Millers planet be ripped to shreds by extreme tidal forces?

If you can survive lava-like temperatures there is another issue for the well-being of Miller's planet from Interstellar. Time passes on the planet 61000 times more slowly than for an observer far ...
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Wouldn't Miller's planet be fried by blueshifted radiation?

In Interstellar, wouldn't Miller's planet be fried by blueshifted radiation? The 61,000x time dilation multiplier would make even cosmic background radiation photons into extreme UV photons. I was ...
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Delta-v for orbital changes around a Kerr black hole

What's the Delta-v to change between the Marginally bound orbit and the innermost stable circular orbit around a Kerr black hole.
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Is there an equation for retrograde equatorial orbital radii around a Kerr black hole as compared to a Schwarzschild black hole?

A non-rotating, non-charged, Schwarzschild black hole has an event horizon with radius $r_s = \frac{2 G M} {c^2}$, where $M$ is the mass of the black hole, $G$ is the gravitational constant, and $c$ ...
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Current status and reference request for the Black Hole Stability Conjecture

The Black Hole Stability Conjecture is one of the most important open problems in the field of General Relativity, and remains open in spite of the advances in the past half century. To test Einstein’...
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Kerr Solution metric ansatz for EFEs

The Schwarzschild metric ansatz is given by $$ds^2=-A(r)dt^2+B(r)dr^2+r^2d \Omega^2$$ where upon applying the Einstein Field Equations $$G_{\mu\nu}=\kappa T_{\mu\nu}$$ we obtain the normal ...
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Interpretation of Angular Momentum flux from stress energy tensor in Black hole superradiance

While studying the superradiance of a scalar field in Kerr geometry, we show that the energy and angular momentum of the Kerr black hole are extracted by the superradiant modes. I understand the ...
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What spins as a black hole? (lame question) [duplicate]

Obviously I am not a physicist. I have seen What is black hole spin? but this is not what puzzles me. If I understand correctly, black hole has only three features (please correct me): angular ...
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Conformally flat slices in Kerr spacetime

I heard some references to ''conformal Kerr'' in general relativity and I'm not sure what this means. It presumably cannot be referring to a conformally flat slice of Kerr spacetime, since the Kerr ...
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Penrose process and the change in irreducible mass

This is a minor confusion. In various lectures notes, for example by Carrol or by Strominger, when discussing the Penrose process of extracting energy from the Kerr black hole, they will exploit the ...
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Condition on particle momentum crossing the Kerr horizon

Around the equation (7.143) in [Carroll] Lecture Notes on General Relativity, the note talks about momentum $p$ of a particle entering the ergosphere and crossing the outer horizon. The claim is that ...
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Derivatives of GHP scalars for typeD spacetimes

Are there any algebraic expressions for $\eth \overline \rho$ and $þ (\overline{\tau}')$ in the GHP formalism? In the specific case of the Kerr metric, by explicit calculation, I managed to prove that ...
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Finding event horizon and ergosphere

I am trying to calculate the event horizon and ergosphere of the Kerr metric. However, I could not seem to find a proper derivation or formula to calculate the event horizon and ergosphere. Could ...
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Outer horizon in the Kerr metric

I have a question about the horizon of a Kerr black hole. Assuming that the metric has a coordinate singularity for $\Delta=0$, namely when $$r_\pm=GM\pm\sqrt{G^2M^2-a^2}$$ how can the outer horizon ...
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What is missing to make this depiction of a Black Hole realistic?

So i am working on a Music video as a FX Artist and part of the job is a Black Hole. Now i am fairly confident that i am just about the only one on the team who cares how accurat the party is. But i ...
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Finding the transformation for the Newman-Penrose formalism

I am working with the Kerr metric (suppose it is $g_{\mu \nu}$) where I want to understand how the Teukolsky master equation is derived using the Newman-Penrose formalism. The original article can be ...
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What does it mean that the inner event horizon of a kerr blackhole is unstable? [duplicate]

I have read that the inner horizon of a Kerr black hole is unstable? What does this mean and what would the inner event horizon become?
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Possible erratum in Hartle's book "Gravity" in example 15.1

I'm reading Hartle's book Gravity (2014), and I think there's an erratum in example 15.1. In this example, he says that for a massive particle at infinity at rest, which starts falling radially ...
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Where is the CTC region of a Kerr Black Hole?

CTCs are found in the region where $r < 0$ . That should be just inside the ring singularity, since in Boyer Lindquist coordinate system $r = 0$ means ring singularity. Does that mean this image ...
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Kerr metric geodesics using EL equations

Let there exist a Kerr metric $ds^2$ in Boyer–Lindquist coordinates such that $$ds^2=-\left(1-\frac{r_sr}{\Sigma}\right)dt^2+\left(\frac{\Sigma}{\Delta}\right)dr^2+\Sigma d \theta^2+\left(r^2+a^2+\...
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A little more detail on the definition of Angular Moment parameter for a Kerr Black Hole

In several places, such as Explain Kerr-Newmann Black Hole Spins in SI Units, the parameter $a$ is defined as: $$a = \frac{Jc}{GM^2}$$ My question is whether the angular momentum J can be defined in ...
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Is accretion disc caused by frame dragging?

Is accretion disc around a Kerr black hole the result of its frame dragging?
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Why is Kerr Singularity ring shaped?

Why is the Kerr singularity like a ring — not a 3-D ellipsoid, or a point, or even a flattened disk? I need an intuitive answer, please.
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Equivalence Principle Frame Dragging

Why do metric equations of a rotating body (like Kerr Metric for black holes or EFE solution for rotating bodies) contain a dt dphi term, leading to rotational frame dragging effects? Please don't ...
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Why is Kerr Spacetime unstable?

How do we know from the Kerr Metric that it is unstable near the Cauchy Horizon? What causes this unstability?
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Crossing a Kerr wormhole

You cannot cross an Einstein Rosen Bridge because it needs faster than light speed to cross it. But the same is not true for a Kerr wormhole, it lies beyond the Cauchy Horizon and you do not need FTL ...
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Watching Kerr Ring Singularity

Can you see light from ring singularity from inside the Cauchy Horizon? In between 2 horizons space and time coordinate swaps places, so the inside region lies at the future. But after crossing Cauchy ...
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Negative $r$ in Boyer-Lindquist system

I am confused about the Boyer Lindquist System. $r = 0$ at the ringularity, and outside that $r$ should be positive (intuitively). But this paper on closed CTCs in Kerr Spacetime claims that $r < 0$...
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Ιn a Kerr Spacetime (for example) how can you relate the simultaneity of a ZAMO observer with the coordinate time $t$?

So bear with me if you can. I will try to type my understanding (which is bad) to this subject (regarding simultaneity), what's exactly the question and why it has came up. Why Reading some papers on ...
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If a very massive object enters in a rotating black hole retrograde orbit should it slow down the black hole's spin?

If a very massive object is orbiting retrograde around a rotating black hole, would it slow down the black hole's spin? Of course, due to its interaction with the black hole's rotating frame, better ...
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Is the spin of a black hole affected by the matter orbiting it?

It's well understood that the moon has an effect on how much the earth spins. My understanding is that if the moon was bigger, it could impact tidal forces to a larger extent, and possibly slow the ...
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What do you see as you look outwards while falling into a Kerr black hole?

Take the Kerr black hole and consider an infalling observer, say equatorial and with zero initial angular momentum for the sake of simplicity. Using the standard metric in Boyer Lindquist coordinates ...
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What happens to the ergospheres of two colliding black holes, right before collision?

Let's assume we have two black holes with equal mass. They move towards each other, each heading towards the center of the other black hole. Both black holes rotate with equal speed. What happens to a ...
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Does the twist of spacetime by a black hole increase over time?

From the Wikipedia page about Ergospheres: As a black hole rotates, it twists spacetime in the direction of the rotation... Does this "twisting up spacetime" add up over time in any ...
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How to plot the cross section of event horizon of hairy kerr black hole?

I was growing through the paper "Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87*" whose link is https://arxiv.org/abs/2103.11417. In the paper it ...
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